The current stock price for XYZ ltd is sh. 25. A European call option with an exercise price of sh. 28 will expire in 160 days. The yield on a 160-day Treasury bill is 5.18%. The standard deviation of annual returns on XYZ’S stock is 21%. Compute the premium for a call option on this stock using Black-Scholes model. You may use c = SN(d1) − XN(d2 )e−rT d1 = ln( s X ) + (r +δ 2 )T δ T

 Assume that the 3.75% US Treasury bond that matures on 15 August 2041 is priced to yield 5.14% for settlement on 15 October 2014. Coupons are paid semi-annually on 15 February and 15 August. The yield-to-maturity is stated on a street-convention semiannual bond basis. This settlement date is 61 days into a 184-day coupon period, using the actual/actual day-count convention. Compute the approximate modified duration and the approximate Macaulay duration for this Treasury bond assuming a 5 bp change in the yield-to-maturity.